Upper bound analysis of asymmetric collapse mechanism of shallow tunnel under seismic load

The aim of this paper is to study the asymmetric collapse mechanism of the overlying rock mass of shallow tunnel under seismic load. Based on the Hoek-Brown failure criterion，combined with the upper bound theorem of the limit analysis and the variational method of the variable endpoints problem，the analytical solution of the asymmetric collapse curve is proposed. The effects of seismic body wave and rock parameters on the asymmetric collapse curve are analyzed. It can be found that，without considering the damage of rock mass，the S-wave will tilt the geometric shape of collapsing block，which is beneficial to restrain the collapse. And the restrain effect is more significant in the rock mass with better mechanical properties. The backward propagation of P-wave will promote the collapse of the rock block and make the geometrical area of the collapsing block smaller. This implies that under seismic load，a smaller range of allowable velocity field can lead to the ultimate failure state of rock mass. The conclusion of this paper will help to provide a safer design and construction guidance for engineering practice.